Here’s a port of the previous Qi II code to Shen.
Run with Hakan Raberg’s 0.1.4 version of shen.clj (Shen implemented in Clojure !).

*
  Accurately calculates N digits of Pi using Machin's formula
  with fixed point arithmetic and variable guards digits.
  Depends on the maths library -->
    http://www.shenlanguage.org/library.html
*
(tc +)
(define arccot-
  {number --> number --> number --> number --> number --> number}
  X N XPOWER    0 _ -> 0
  X N XPOWER TERM 1 -> (+ (arccot- X (+ N 2) (floor (/ XPOWER X))
                                     (floor (/ XPOWER N)) 0)
                          (floor (/ XPOWER N)))
  X N XPOWER TERM 0 -> (- (arccot- X (+ N 2) (floor (/ XPOWER X))
                                      (floor (/ XPOWER N)) 1)
                          (floor (/ XPOWER N))))
(define arccot
  {number --> number --> number}
  X UNITY -> (let XPOWER (floor (/ UNITY X))
                  (arccot- (* X X) 1 XPOWER (floor XPOWER) 1)))
(define machin-pi
  {number --> number}
  DIGITS -> (let GUARD (+ 10 (ceiling (log' DIGITS 10)))
                 UNITY (expt 10 (+ DIGITS GUARD))
                 (floor (/ (* 4 (- (* 4 (arccot 5 UNITY))
                                   (arccot 239 UNITY)))
                           (expt 10 GUARD)))))
(1+) (time (machin-pi 100))
run time: 2.56899999999996 secs
31415926535...4350265344N : number